The compression characteristics of a passive self-similar compressor consisting of a dispersion-decreasing fiber (DDF) and a compensative fiber are numerically investigated. The results show that the group-velocity dispersion (GVD) of the compensative fiber has a periodic influence on the compression factor and peak power of the compressed pulse. That is, the pulse energy is concentrated, then dispersed, and then concentrated again periodically. Every time the energy is concentrated, the pulse width reaches its compression limit. With the increase of the GVD value of the compensative fiber, the period interval increases and more energy is transferred within a period. On the other hand, an increase of the nonlinearity of the compensative fiber leads to a decrease of the compression factor, which is not conducive to pulse compression. Moreover, the degree of self-similar evolution is decided by the length of the DDF. A suitable evolution degree and optimal DDF length cause the pulse to reach a maximum compression limit. In addition, the optimal compensative fiber length increases with the degree of self-similar evolution and decreases with the GVD value of the compensative fiber, although it has nothing to do with the nonlinearity of the compensative fiber. By optimizing the parameters of the compensative fiber and the length of the DDF, the pulse width attains a compression limit and a high-quality pulse is obtained.